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Workbook

SYSTEMS OF LINEAR EQUATIONS

A linear equation in two variables has an infinite number of solutions that form a line in rectangular
coordinate system. Two or more linear equations form a system of linear equations. For example:
x 3y   5

2x 4y 10 

A solution to a system of linear equations is an ordered pair that is a solution to each individual linear
equation.

EXAMPLE 1: Determine whether the ordered pairs are solutions to the system.

x y   6

3x y   2

a)  2, 4   b) 0, 6 

A solution to a system of two linear equations may be interpreted graphically as a point of intersection
between the two lines. Graphing the lines from Example 1 , we have

x y   6

3x y   2

Notice that the lines intersect at  2, 4   . Graph the lines.

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